What Is A Conjecture
What is a Conjecture ?
Inductive reasoning is a type of reasoning that allows you to reach conclusions based on a pattern of a specific examples or past events. A conclusion reached by using inductive reasoning is called CONJECTURE.
For each sequence below, find the next term by first finding a pattern. Then using a pattern, make a conjecture about the next term.
Example number one :
Given sequence : 1, 8, 27, 64 , ____
Conjecture : Y = X^3
Verifying Conjecture :
Let X = 1 then Y = 1^3 = 1
Let X = 2 then Y = 2^3 = 8
Let X = 3 then Y = 3^3 = 27
Let X = 4 then Y = 4^3 = 64
What is the next number in the series ?
Let X = 5 then Y = 5^3 = 125
The next number in the series is 125.
Example number two :
Given sequence : 3, 5, 11, 29, ____
Conjecture : Y = 3^X + 2
Verifying Conjecture :
Let X = 0 then Y = 3^0 + 2 = 1 + 2 = 3
Let X = 1 then Y = 3^1 + 2 = 3 + 2 = 5
Let X = 2 then Y = 3^2 + 2 = 9 + 2 = 11
Let X = 3 then Y = 3^3 + 2 = 27 + 2 = 29
What is the next number in the series ?
Let X = 4 then Y = 3^4 + 2 = 81 + 2 = 83
The next number in the series is 83.
Example number three :
Given sequence : 3, 5, 7, 9, ___
Conjecture : Y = 2X + 3
Verifying Conjecture :
Let X = 0 then Y = 2(0) + 3 = 3
Let X = 1 then Y = 2(1) + 3 = 5
Let X = 2 then Y = 2(2) + 3 = 7
Let X = 3 then Y = 2(3) + 3 = 9
What is the next number in the series ?
Let X = 4 then Y = 2(4) + 3 = 11
The next number in the series is 11
For your practice exercises try to find the conjecture of the following series:
(1) 5, 8, 11, 14
(2) 1, 4, 16, 64
(3) 2, 3. 5, 9
(4) 3, 6, 9, 12
(5) 1, 2. 4. 8. 16
Answers :
1) Y = 3X + 5
2) Y = 2 ^2X
3) Y = 2^X + 1
4) Y = 3X
5) Y = 2^X
Reference : GEOMETRY by Neo Asia Publishing